# Mathematics Questions and Answers – Conditional Probability

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Conditional Probability”.

1. If E and F are two events associated with the same sample space of a random experiment then P (E|F) is given by _________
a) P(E∩F) / P(F), provided P(F) ≠ 0
b) P(E∩F) / P(F), provided P(F) = 0
c) P(E∩F) / P(F)
d) P(E∩F) / P(E)

Explanation: E and F are two events associated with the same sample space of a random experiment.
The value of P (E|F) = (E∩F) / P(F), provided P(F) ≠ 0. We know that if P(F) = 0, then the value of P(E|F) will reach a value which is not defined hence it is wrong option. Also, P(E∩F) / P(F) and P(E∩F) / P(E) are wrong and do not equate to P(E|F).

2. Let E and F be events of a sample space S of an experiment, if P(S|F) = P(F|F) then value of P(S|F)
is __________
a) 0
b) -1
c) 1
d) 2

Explanation: We know that P(S|F) = P(S∩F) / P(F). (By formula for conditional probability)
Which is equivalent to P(F) / P(F) = 1, hence the value of P(S|F) = 1.

3. Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E∩F) = 0.2, then P(E|F) ?
a) 2/3
b) 1/3
c) 3/4
d) 1/4

Explanation: We know that P(E|F) = P(E∩F) / P(F). (By formula for conditional probability)
Value of P(E∩F) is given to be 0.2 and value of P(F) is given to be 0.3.
P(E|F) = (0.2) / (0.3).
P(E|F) = 2 / 3.
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4. Given that E and F are events such that P(E) = 0.5, P(F) = 0.4 and P(E∩F) = 0.3, then what will be the value of P(F|E)?
a) 2/5
b) 3/5
c) 3/4
d) 2/4

Explanation: We know that P(F|E) = P(E∩F) / P(E). (By formula for conditional probability)
Value of P(E∩F) is given to be 0.3 and value of P(E) is given to be 0.5.
P(F|E) = (0.3) / (0.5).
P(F|E) = 3 / 5.

5. Let E and F be events of a sample space S of an experiment, if P(S|F) = P(F|F), then value of P(F|F)
is __________
a) 0
b) -1
c) 1
d) 2

Explanation: We know that P(S|F) = P(S∩F) / P(F). (By formula for conditional probability)
Which is equivalent to P(F|F) = P(F) / P(F) = 1, hence the value of P(F|F) = 1.
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6. If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________
a) 3/5
b) 2/3
c) 1/2
d) 1

Explanation: We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
Also P(A∪B) = P(A)+P(B) – P(A∩B). (By formula of probability)
$$\Rightarrow$$ 8/11 = 7/11 + 6/11 – P(A∩B)
$$\Rightarrow$$ P(A∩B) = 13/11 – 7/11
$$\Rightarrow$$ P(A∩B) = 6/11
P(A|B) = (6/11) / (6/11).
P(A|B) = 1.

7. If P(A) = 1/5, P(B) = 0, then what will be the value of P(A|B)?
a) 0
b) 1
c) Not defined
d) 1/5

Explanation: We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
The value of P(B) = 0 in the given question. As the value of denominator becomes 0, the value of P(A|B) becomes un-defined.

8. If P(A) = 5/13, P(B) = 7/13 and P(A∩B) = 3/13, evaluate P(A|B).
a) 1/7
b) 3/7
c) 3/5
d) 2/7

Explanation: We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
Which is equivalent to (3/13) / (7/13), hence the value of P(A|B) = 3/7.

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